A beginner's guide to Feynman diagrams

Feynman diagrams are designed as a way both to illustrate those electromagnetic interactions, and to explore and quantify the many variants that ... SubscribetoBBCScienceFocusMagazinePreviousIssuesPodcastQ&ASearchNoresultNewsFuturetechNatureSpaceHumanbodyEverydaysciencePlanetEarthNewslettersSubscribetoBBCScienceFocusMagazinePreviousIssuesPodcastQ&AHomeEverydayscienceAbeginner'sguidetoFeynmandiagrams❚Allproductswerechosenindependentlybyoureditorialteam.Thisguidecontainsaffiliatelinksandwemayreceiveacommissionforpurchasesmade.PleasereadouraffiliatesFAQpagetofindoutmore.Abeginner'sguidetoFeynmandiagramsByBrianCleggPublished:01stNovember,2021at16:00Try3issuesofBBCScienceFocusMagazinefor£5!InthisextractfromTenPatternsThatExplainTheUniverse,sciencewriterBrianCleggexplainshowRichardFeynman'seponymousdiagramsnotonlyillustratecomplexparticleinteractions,butcanmakecalculationseasier,too.ShareonfacebookShareontwitterShareonwhatsappShareonredditEmailtoafriendQuantumphysicsdescribestheworkingsoftheUniverseatthelevelofthetinyparticles,suchaselectronsandphotonsoflight,thatmakeitup.Mostofoureverydayexperiencescomefromtheinteractionofmatterparticleswitheachotherandwithlight,whichcanbeexplainedbyquantumelectrodynamics(QED).AdvertisementThisdetailedtheorywouldwintheNobelPrizeinPhysicsforRichardFeynman,JulianSchwinger,andSin-ItiroTomonaga.Muchoftheiroriginalthinkinginvolvedcomplexmathematics,asitwasnecessarytodealwithavastnumberofpotentialinteractions,eachwithdifferentprobabilities.ButFeynmanrealisedthattheseinteractionscouldberepresentedbysimplediagrams–patternsthatdefinetheinterplayoflightandmatter.NotonlydidtheymakeQEDmorecomprehensible,Feynmandiagramsalsoprovidedavisualtoolformakingotherwiseimpossiblecalculationspractical.Eachdiagramcombinesaseriesoflineswhere,forexample,straightlinesrepresentmatterparticlesandwavylinesarephotons.Thesearepatternsinspace-time,buttheyrepresenttheinteractionofparticles.Asimpleexamplemightshowtwoelectronsrepellingeachotherelectromagnetically,withaphotonpassingbetweenthemasaforcecarrier.Feynman’sdiagramswerenecessarytoreflectthestrangebehaviourofquantumparticles,whichbearsnoresemblancetotheactionofthephysicalobjectsthataremadeupofthem.Toseewhythediagramsweresosignificant,weneedtotakeastepbacktowhatmakesquantumphysicsappearsobizarre.Readmoreaboutquantumphysics:Quantumfieldtheory:"Anunholycrossbreedbetweenquantumphysicsinabadmoodandeverybuttonyouneverpushonacalculator"ThebizarrelinkbetweenbirdmigrationandquantumphysicsHowaquantumcomputerisdifferentfromyourlaptop,explainedbyascientistQED:QuantumelectrodynamicsQuantumphysicsbeganwithEinstein’srealisationthatphotonswerereal,soonexpandingtoexplainthestructureoftheatom.Itisthescienceoftheverysmall,whererealityseemsnottohavethedeterministiccertaintyoftheworldwetypicallyobserve,butratherprobabilitiesdominate.Quantumelectrodynamics,whichiswhereFeynmandiagramswerefirstused,considerstheinteractionsofquantumparticlesthataredependentonelectromagnetism.Incommonusage,‘electromagnetism’soundslikeitisjustaboutelectricityandmagnetism,whichinasenseitis.Butweneedtounderstandthatitisresponsibleforthevastbulkofeverydayinteractionsintheworldthatweexperience.Lightisanelectromagneticphenomenon.Similarly,mostinteractionsbetweenatomsiselectromagnetic.So,forexample,whenyousitonachairitistheelectromagneticforceactingbetweentheatomsofthechairandtheatomsinyourbodythatpreventyouratomsfromsimplyslippingpastthoseinthechair.TheelectromagneticforceisoneofthefourfundamentalforcesoftheUniverse.Theotherthreearegravity,andthestrongandweakinteractions–thesetwoforcesareinvolvedinthenucleusofatoms.Wetendtothinkofgravityasprettyoverwhelming,yetinfactitisbyfartheweakestofthefourforces,billionsofbillionstimesweakerthanelectromagnetism.Ifyoudoubtthis,justthinkofafridgemagnet.TheentiregravitationalpullofEarthisattemptingtopullittothefloor.Allthatholdsittothefridgeistheelectromagneticforcefromitstinymagnet.Themagnetwins.Gravityistheweakestforce–evenatinyfridgemagnetcanwinagainstit©GettyImagesInquantumtheory,forcespassfromplacetoplaceasaresultofso-calledforcecarriers–particlesthattravelbetweenthetwoobjectsthatareattractingorrepellingeachother.Thisiswhy,forexample,amagnetcanattractapieceofironatadistance.Perhapssurprisingly,theforcecarrierofelectromagnetismisaparticlewehavealreadymet­–thephoton.Weusuallygetintroducedtothephotonastheparticleoflight,buteverytimethereisanelectromagneticinteractionbetweenmatterparticlesaflowof‘virtualphotons’betweentheparticlesproducetheeffectofaforce.Theterm‘virtual’hereisdecidedlymisleading.Itsoundsasifitmeansthattheparticlesdon’texist.Whatitreallyrefersto,though,isthatthephotonsaren’teverobserved,astheypassfromoneparticletoanotherwithoutescaping.Asaresult,nearlyeveryelectromagneticinteraction–whichmeansnearlyeveryinteractionofmatternotinvolvinggravity–istheresultofamatterparticleemittingaphoton,oramatterparticleabsorbingaphoton,orboth.FeynmandiagramsAsimpleFeynmandiagram,showingparticlesrepresentedbystraightlinesandaphotonrepresentedbyawavyline.Inthiscase,theverticalaxisisspaceandthehorizontalaxisistime©Romainbehar,CC0,viaWikimediaCommonsFeynmandiagramsaredesignedasawaybothtoillustratethoseelectromagneticinteractions,andtoexploreandquantifythemanyvariantsthatthestrangenatureofquantumphysicsprovidesthatwouldnotbeexpectedotherwise.Onthediagrams,matterparticlesarerepresentedbystraightlinesandphotonsaswigglylines.(ThereareothertypesoflinewhentheuseofthediagramisexpandedbeyondsimpleQED.)Thereisnotaclearconventiononwhichaxisistimeandspace.Quiteoften,timeistheverticalaxisinaFeynman,butwhereit’smoreconvenient,itcanbethehorizontalaxisinstead.Themostcommonelementsshownonsuchadiagramarethataphotontravelsfromonelocationtoanother;amatterparticle(atitssimplest,anelectron)travelsfromoneplacetoanother;oramatterparticlegivesofforabsorbsaphoton.Almosteverythingcanbebuiltupfromthesesimplecomponents.Butbecauseoftheodditiesofquantumphysics,anapparentlysimpleactioncanresultinawholeplethoraofdiagrams.Takeanapparentlysimpleexampleoftwoelectronsmoving.Weknowwheretheystartandwheretheyfinish.ButhowdotheygetfrombeinglocatedatAandBtobeingatCandD?ThesimplestpossibilityistheelectronfromAendsupatC,andthatfromBatD.AnotherprobabilityisthattheelectronfromAendsupatDandtheonefromBatC.Feynmandiagramsforthepossibilitiesoftwoparticlesstartingatonelocationandendingatanotherwithoutinteracting©RichardPalmerNotethatwecan’ttellwhichhashappenedaswedon’tknowtheroutetheelectronstook,nordoweknowwhichelectroniswhich.Oneofthedefinitivethingsaboutquantumparticles,suchaselectrons,isthattheyhavenodistinguishingfeatures.Theyaretrulyidentical.That’sstraightforwardenough,butthereareotherpossibilities.Electrons,likeotherquantumparticles,canundergoaprocessknownasscattering.Thisisoftenrepresentedasoneelectronbouncingofftheother,likeapairofballsonasnookertable.However,electronsareelectricallychargedparticles,andelectromagneticinteractionworksthroughphotons.So,anotherdiagramwouldshowaphotonpassingfromoneelectrontotheother,asaresultchangingthepathsoftheelectronssothattheyendupatCandD.Thiscouldariseinanumberofways.Feynmandiagramsforthepossibilitiesoftwoparticlesstartingatonelocationandendingatanotherwithanelectromagneticinteraction©RichardPalmerEachofthedifferentpossiblediagramswillhaveaprobabilityattachedtoit.Asweaddinmoreunlikelypossibilities,theoutcomebecomescloserandclosertoreality.It’samusingthatquantumphysicsisinonesensethemostaccuratesciencewehave.AsFeynmanonceobserved,thedifferencebetweenitspredictionsandrealityarecomparabletothewidthofahaironthescaleofthedistancebetweenNewYorkandLosAngeles.Yetontheotherhand,thepredictionsofquantumphysicsarebasedonprobabilities,andthoughwecancomenearertotheactualvalueitwillalwaysbethelimitoftakingeverypossiblediagramintoconsideration,ratherthanasimpleoutcome.AlthoughFeynmandiagramssometimeshavearrowsindicatingadirectionoftravel,theyareoftennotnecessary.Take,forexample,thephotontravellingbetweenelectronsinthediagramsshownabove.Itisperfectlyacceptabletosaythatthephotontravelsinthedirectionthathasittravellingintothefuture,butinpractice,themathematicsusedtomakethecalculationdoesn’tcarewhetherthephotontravelsforwardorbackwardintime.Justasthediagramsdon’tusuallydistinguishadirection,sothephotonisdescribedasbeing“exchanged”bytheparticles,ratherthantravellingfromaspecificparticletotheotherone.Wewon’tgothrougheverypossiblediagramforthissimpleinteraction(infactitwouldbeimpossible,andevenattemptingitwouldbehighlytedious).Butjusttoshowhowmoreandmorecomplexitycouldbeaddedin,anextpossibilitycouldbetohavetwophotonsexchangedalongtheway,producingapairofscatteringevents.Bythetimewegetdowntoaneventlikethis,thecontributionisalreadysomethinglikeonepartin10,000.Feynmandiagramforthepossibilityoftwoparticlesstartingatonelocationandendingatanotherwithtwoelectromagneticinteractions©RichardPalmerAdvertisementNote,incidentally,thatthediagramsaremorethanvisualillustrations–theyareamechanismtobasecalculationson.Theactualcalculationscanbecomepainfullymessy,butthediagramsprovidethepatternstogroundtheminanapproachablefashion.TenPatternsThatExplainTheUniversebyBrianCleggisoutnow(£25,MITPress). BuynowfromAmazonUK,WaterstonesorBookshop.org Readmoreaboutparticlephysics: Whatisantimatter,andwhyisitmissingfromtheUniversetoday? 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